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1972 AHSME Problems/Problem 3

Revision as of 00:53, 7 November 2020 by Lopkiloinm (talk | contribs) (→‎Solution)

Problem 3

If $x=\dfrac{1-i\sqrt{3}}{2}$ where $i=\sqrt{-1}$, then $\dfrac{1}{x^2-x}$ is equal to

$\textbf{(A) }-2\qquad \textbf{(B) }-1\qquad \textbf{(C) }1+i\sqrt{3}\qquad \textbf{(D) }1\qquad \textbf{(E) }2$

Solution

Using DeMoivre's theorem, we can calculate $x^2=\frac{1+i\sqrt{3}}{2}$ The denominator is therefore $-1$ which makes the answer 

\[\boxed{\textbf{(C) }-1.\] (Error compiling LaTeX. Unknown error_msg)

~lopkiloinm

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